Abstract
The d-c.e. (difference of c.e.) and dbc (divergence bounded computable) reals are two important subclasses of Δ\(_{\rm 2}^{\rm 0}\)-reals which have very interesting computability-theoretical as well as very nice analytical properties. Recently, Downey, Wu and Zheng [2] have shown by a double witness technique that not every Δ\(_{\rm 2}^{\rm 0}\)-Turing degree contains a d-c.e. real. In this paper we show that the classes of Turing degrees of d-c.e., dbc and Δ\(_{\rm 2}^{\rm 0}\) reals are all different.
This work is supported by DFG (446 CHV 113/240/0-1) and NSFC (10420130638).
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Rettinger, R., Zheng, X. (2005). On the Turing Degrees of Divergence Bounded Computable Reals. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_51
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DOI: https://doi.org/10.1007/11494645_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26179-7
Online ISBN: 978-3-540-32266-5
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